What is the significance of the title "Agora"?

It's from the Greek word "Agora", the meaning of which was

"gathering place" or "assembly".

Many sources discuss and confirm this, but I like Roger Ebert's description the best:

[Hypatia's] father Theon (Michael Lonsdale) was the curator of the Library of Alexandria, which had as its mission "collecting all the world's knowledge." Scholars traveled there from across the ancient world, doing research and donating manuscripts. It was destroyed by Christians in 391 A.D., and "Agora" takes place in the years surrounding that incalculable loss.

The film's title refers to a name for the public assembly places in ancient Greek city-states. The library was such an agora, and we see Hypatia teaching a class of young men who listen to her with open admiration.

Per wikipedia

The title of the film takes its name from the agora, a gathering place in ancient Greece, similar to the Roman forum.

This was explicitly confirmed in a huffpo interview with the film's lead actress; Rachel Weisz

W&H: The film was huge in Spain. A blockbuster. Can you explain the word Agora?

RW: It’s an ancient Greek word that means market place. It’s a place where people met. And I guess the premise of the film, or the conceit of the title is, the earth is an Agora. It’s a meeting place for humans who don’t get along.